Corollary 2 (Tight  and Tractable Decomposition  Functions for JSS Vector Fields)  
 Suppose \(f(\cdot )\)  is continuously differentiable and Jacobian sign-stable (JSS) [1]}, i.e.,  \(\forall i \in \mathbb {N}_{n_x}, \forall j \in \mathbb {N}_{n_z}, J^f_{ij}(z)\triangleq \frac{\partial f_i}{\partial z_j}(z)\ge 0, \forall z \in \mathbb {I}\mathcal {Z}\)  or \(J^f_{ij}(z)\triangleq \frac{\partial f_i}{\partial z_j}(z)\le 0, \forall z \in \mathbb {I}\mathcal {Z}\) . Then, the following statements hold :
